🧮 algebra

1. **State the problem:** Solve for $a$ in the equation $2a + 0.8\overline{3} = 4.6\overline{6}$. 2. **Understand repeating decimals:**

1. **State the problem:** Find the equation of the secant line passing through the points $(-3, g(-3))$ and $(5, g(5))$ on the curve defined by $g(x) = x^2 - 9x$. 2. **Find the coo

1. **State the problem:** Solve for $x$ in the equation $$\frac{8x}{3} = \frac{x}{5} - 74$$. 2. **Write down the equation:** $$\frac{8x}{3} = \frac{x}{5} - 74$$.

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic equation formula or factorization method. Here, factorization is simpler.

1. **Stating the problem:** We need to expand the algebraic expressions given: (e) $ (5 - 8x)^2 $

1. **State the problem:** We need to find the value of the expression $$\frac{7 - 3x}{2}$$ when $$x = -9$$. 2. **Substitute the value of $$x$$:** Replace $$x$$ with $$-9$$ in the e

1. **Stating the problem:** We need to expand and simplify the following expressions: a) $ (x - y)^2 $

1. **State the problem:** We need to find the value of the expression $6 - 3x$ when $x = -4$. 2. **Write the expression:** The expression is $6 - 3x$.

1. **State the problem:** We need to evaluate the sum $$E \approx t = \sum_{t=5}^{14} \left(50t^{1.6} + 8t\right)$$.

1. **State the problem:** We are given the profit function for a company producing phones: $$P(x) = -1.5x^2 + 10.5x - 4$$

1. **State the problem:** Solve for $x$ in the equation $3(x+9)-(15-x)=8(x+1)$. 2. **Apply the distributive property:**

1. **Problem:** Calculate the products and simplify the radicals as requested. 2. **Step a) Calculate $\sqrt{7} \times \sqrt{8}$:**

1. **State the problem:** We need to complete the description of the piecewise function $f(x)$ based on the graph with three segments:

1. **State the problem:** We need to find the equation of a mystery line given several clues. 2. **Analyze Clue #1:** The mystery line is perpendicular to the line $$y = -\frac{2}{

1. **State the problem:** Solve the equation $$980 = (40) \cdot 8$$. 2. **Understand the equation:** The equation shows a multiplication of 40 and 8 on the right side, which should

1. **State the problem:** We have an arithmetic sequence defined by the rule $x_n = an + b$, where $a$ and $b$ are constants. We need to find $a$ and $b$ given the sequence terms:

1. **State the problem:** Solve the equation $8 \cdot (4 - 40 + 4) = 120$. 2. **Simplify inside the parentheses:** Calculate $4 - 40 + 4$.

1. **State the problem:** Simplify the expression $$\left( \frac{1}{x^2 + xy} + \frac{2}{x - y} - \frac{1}{x^2 - xy} \right) \cdot \frac{x^3 - 2x^2 y + xy^2}{x^2 + xy - y}$$

1. **State the problem:** Find the Least Common Multiple (LCM) of the algebraic expressions $10 + 10x$ and $(2x + 2)(5x - 10)$. 2. **Rewrite expressions to factor form:**

1. **State the problem:** Find the Least Common Multiple (LCM) of the algebraic expressions $(3x + 9)(4x + 4)$ and $7x + 7$. 2. **Rewrite expressions in factored form:**

1. The problem asks to find which equation has a constant of proportionality equal to 4. 2. The constant of proportionality $k$ in an equation of the form $y = kx$ relates $y$ and